How did Matthew conclude that Isaiah 7:14 refers to Jesus?

Your consternation may stem from not considering that time has no meaning in the realm where God resides. As with most Old Testament Prophesy it may span a period of days, years or even centuries, as we see in the book of Daniel (as an example ) and in the New Testament book of the Revelation. All of the time of the Earth will not even be a blip in Eternity.

It also must be remembered that Jesus told them:

John 14:26 But the Comforter, which is the Holy Ghost, whom the Father will send in my name, he shall teach you all things, and bring all things to your remembrance, whatsoever I have said unto you.

It also must be remembered that they were still waiting after centuries for the Messiah, prophesied in the prophets. That they were used to not having Prophesy fulfilled quickly is explained by David Guzik in his commentary of the entire Bible, concerning the Passage you asked about, which I have included for your perusal.

(13-16) The LORD's sign to Ahaz: the sign of Immanuel. Then he said, "Hear now, O house of David! Is it a small thing for you to weary men, but will you weary my God also? Therefore the Lord Himself will give you a sign: Behold, the virgin shall conceive and bear a Son, and shall call His name Immanuel. Curds and honey He shall eat, that He may know to refuse the evil and choose the good. For before the Child shall know to refuse the evil and choose the good, the land that you dread will be forsaken by both her kings."

a. Is it a small thing for you to weary men, but will you weary my God also? The rulers of Judah treated other people poorly, but they treated the LORD even more poorly. If many of us expressed the same distrust we have towards the LORD towards other people, we might get a punch in the nose!

i. "How heartily angry is the prophet, how blessedly blown up in this case to so great dishonor done to God! We should be so too." (Trapp)

ii. Spurgeon speaks well to this point: "Did I not hear some one say, 'Ah, sir, I have been trying to believe for years.' Terrible words! They make the case still worse. Imagine that after I had made a statement, a man should declare that he did not believe me, in fact, he could not believe me though he would like to do so. I should feel aggrieved certainly; but it would make matters worse if he added, 'In fact I have been for years trying to believe you, and I cannot do it.' What does he mean by that? What can he mean but that I am so incorrigibly false, and such a confirmed liar, that though he would like to give me some credit, he really cannot do it? With all the effort he can make in my favour, he finds it quite beyond his power to believe me? Now, a man who says, 'I have been trying to believe in God,' in reality says just that with regard to the Most High."

b. Therefore the Lord Himself will give you as sign: Behold, the virgin shall conceive and bear a Son, and shall call His name Immanuel. This is one of the most famous prophecies regarding the birth of Jesus the Messiah in the Bible. It also illustrates a principle of prophecy, that prophecy may have both a near fulfillment and a far fulfillment.

i. Spurgeon said of this passage, that it is said to be "One of the most difficult in all the Word of God. It may be so; I certainly did not think it was until I saw what the commentators had to say about it, and I rose up from reading them perfectly confused."

ii. "It is characteristic of predictive prophecy that it often mingles different times together in one composite picture" (Martin)

c. The near fulfillment of this prophecy centered around Ahaz, Jerusalem, and the attack from Israel and Syria. For Ahaz, the sign centered around a time span (For before the Child shall know to refuse the evil and choose the good, the land that you dread will be forsaken by both her kings). Simply put, God would give Ahaz a sign that within a few years, both Israel and Syria would be crushed. This was a sign of deliverance to Ahaz.

i. Many commentators think that this was immediately fulfilled when a young woman in the royal household shortly married, conceived a son, and unknowingly naming him "Immanuel." Before this boy came to eat solid food, Israel and Syria were be defeated. It is also possible that God is just referring in a figurative way to a year or two period of time.

ii. "The name 'Immanuel' was a rebuke to Ahaz. If 'God is with us,' then why should he have feared the enemy?" (Wolf)

iii. "The 'sign' of the child, therefore, constitutes an indication that the all-sovereign and all-knowing God has the situation completely in hand, and it rebukes the king's lack of faith in him." (Grogan)

d. The far or ultimate fulfillment of this prophecy goes far beyond Ahaz, to announce the miraculous virgin birth of Jesus Christ.

i. We know this passage speaks of Jesus because the Holy Spirit says so through Matthew: "Behold, the virgin shall be with child, and bear a Son, and they shall call His name Immanuel," which is translated, "God with us." (Mat. 1:23)

ii. We know this passage speaks of Jesus because the prophecy is addressed not only to Ahaz, but also to David's entire house (O house of David!).

iii. We know this passage speaks of Jesus because it says the virgin shall conceive, and that conception would be a sign to David's entire house. Those who deny the virgin birth of Jesus like to point out that the Hebrew word translated virgin (almah) can also be translated as "young woman." The idea is that Isaiah was simply saying that a "young woman" would give birth, not a virgin. While the near fulfillment may have reference to a young woman giving birth, the far or ultimate fulfillment clearly points to a woman miraculously conceiving and giving birth. This is especially clear because the Old Testament never uses the word in a context other than virgin and because the Septuagint translates it categorically virgin (parthenos).

iv. We know this passage speaks of Jesus because it says He will be known as Immanuel, meaning "God with Us." This was true of Jesus in fact, not only as a title. Immanuel speaks both of the deity of Jesus (God with us) and His identification and nearness to man (God with us).

e. Jesus is truly Immanuel, God with us. "Christ, indeed, was not called by this name Immanuel that we anywhere read of . . . but the import of this name is most truly affirmed and acknowledged to be fully made good in him." (Trapp)

i. "He is, therefore, called God with us, or united to us; which cannot apply to a man who is not God . . . it denotes not only the power of God, such as he usually displays by his servant, but a union of person, by which Christ became God-man." (Calvin)

ii. "In what sense then, is Christ GOD WITH US? Jesus is called Immanuel, or God with us, in his incarnation; God with us, by the influences of his Holy Spirit, in the holy sacrament, in the preaching of his word, in private prayer. And God with us, through every action of our life, that we begin, continue, and end in his name. He is God with us, to comfort, enlighten, protect, and defend us, in every time of temptation and trial, in the hour of death, in the day of judgment; and God with us and in us, and we with and in him, to all eternity." (Clarke)

As with most Old testament Prophesies they span a long time in our world, but almost nothing in eternity. as an example take the prophesy in Daniel chapter 9:

Daniel 9:22through 27 And he informed me, and talked with me, and said, O Daniel, I am now come forth to give thee skill and understanding. 23 At the beginning of thy supplications the commandment came forth, and I am come to shew thee; for thou art greatly beloved: therefore understand the matter, and consider the vision. 24 Seventy weeks are determined upon thy people and upon thy holy city, to finish the transgression, and to make an end of sins, and to make reconciliation for iniquity, and to bring in everlasting righteousness, and to seal up the vision and prophecy, and to anoint the most Holy. 25 Know therefore and understand, that from the going forth of the commandment to restore and to build Jerusalem unto the Messiah the Prince shall be seven weeks, and threescore and two weeks: the street shall be built again, and the wall, even in troublous times. 26 And after threescore and two weeks shall Messiah be cut off, but not for himself: and the people of the prince that shall come shall destroy the city and the sanctuary; and the end thereof shall be with a flood, and unto the end of the war desolations are determined. 27 And he shall confirm the covenant with many for one week: and in the midst of the week he shall cause the sacrifice and the oblation to cease, and for the overspreading of abominations he shall make it desolate, even until the consummation, and that determined shall be poured upon the desolate.

This explanation was given to Daniel by the Angel Gabriel, while in captivity sometime around 600 BC, and covers centuries, and yet Jesus said:

Mat 24:15 When ye therefore shall see the abomination of desolation, spoken of by Daniel the prophet, stand in the holy place, (whoso readeth, let him understand:)

when explaining the end times to his disciples.

This has become quite long otherwise I would give you more examples, but you can search out those for yourself.

In closing remember that there were many teachers of the Jewish faith, (Rabboni) and every Jew was schooled in the Prophets, so when the Holy Spirit taught them, and brought all thins back to their remembrance this surely would have caused them some consideration and the connection of the birth of Jesus to the prophesy of Isaiah was probably discussed among the Apostles.

Hope this helps .